Hi,
If a qualifying conversion takes place then the majority of the work completed by a builder would be at the reduced rate of VAT. This would include the conversion of a barn into a self contained dwelling.
Buildings and construction (VAT Notice 708)
If the conditions are met for a qualifying conversion then the reduced rate of VAT should be applied by the builder and this is not optional or subject to change.
HMRC can't get involved in a dispute between two parties however and this would need to be resolved between yourself and the builder or through legal channels.
Thank you.